ON THE DEGREE OF CURVES VANISHING AT FAT POINTS WITH EQUAL MULTIPLICITIES

Nguyen Chanh TU; Do Trong HOANG

doi:10.2206/kyushujm.67.17

Kyushu Journal of Mathematics

Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116

67-1

ON THE DEGREE OF CURVES VANISHING AT FAT POINTS WITH EQUAL MULTIPLICITIES

Nguyen Chanh TU, Do Trong HOANG

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Keywords: Nagata's conjecture, good subdivision, m-triangular, multiplicities, fat points, minimal degree

JOURNAL FREE ACCESS

2013 Volume 67 Issue 1 Pages 17-27

DOI https://doi.org/10.2206/kyushujm.67.17

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Abstract

The problem of determining the least degree of plane curves vanishing at given points with certain multiplicities is fascinating and difficult. In 1959,Nagata gave a conjecture on the lower bound of the degree. Since then, many mathematicians have focused on solving the conjecture for several special cases. In this paper, we show several results on determining the least degree for certain cases of equal multiplicities.

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